If the two matrices [[1, 0, 1], [0, x, 1], [0, 1, x]] and [[x, 1, 0], [x, 0, 1], [0, x, 1]] have the same determinant, then the value of x is
- A. 1/2
- B. $\sqrt{2}$
- C. +- 1/2
- D. +- 1/$\sqrt{2}$
Answer: A. 1/2
Explanation: Det1 = 1(x² - 1). Det2 = x(-x) - 1(x) = -x² - x. x² - 1 = -x² - x. 2x^2 + x - 1 = 0. (2x-1)(x+1) = 0. x = 1/2 or -1.